KATE KELLY and ALAN RAPPEPORT

With President Trump’s promise to repeal and replace the Affordable Care Act nearly dead, administration officials are scaling back their ambitions to cut the corporate tax rate sharply, apparently taking a more pragmatic approach as they scramble to secure a major legislative victory this year.

In recent days, discussions among Mr. Trump’s economic advisers over promised tax cuts for corporations and individuals have taken on new urgency, a person who has been briefed on the matter said. One crucial point of discussions in the coming days, the person said, will be the proposed business tax rate. In April, a White House policy paper pegged it at 15 percent for corporations and small businesses alike. The current rate is 35 percent.

But now the proposed business tax rate is “drifting higher,” this person said, and may end up in the low 20 percent range.

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With the health care plan seemingly in ruins, this person said, the tax overhaul will very likely take top priority. Steven T. Mnuchin, the Treasury secretary, and Gary D. Cohn, the director of the National Economic Council, are communicating daily over the tax proposal with the aim of drafting a bill to be introduced on the House floor in early September. To ensure the support of influential lawmakers in both chambers of Congress, the two officials are meeting weekly to discuss the bill’s intricacies in a group being referred to as the “Big Six:” House Speaker Paul Ryan; Kevin Brady, chairman of the House Ways and Means Committee; Senate Majority Leader Mitch McConnell; and Orrin Hatch, chairman of the Senate Finance Committee.

The final tax rate will depend somewhat on whether corporations are permitted to deduct their interest expenses — a hot-button issue that has caused great concern for businesses that rely heavily on debt.

A White House spokeswoman, Natalie Strom, said, “Discussions between the White House and Congress are progressing in a very positive direction. We have always had more areas of agreement than disagreement, and we feel confident we will develop a unified plan that will deliver on our goals of economic growth and tax relief for hard-working middle-income families.”

A corporate tax rate in the 20 percent range would put the Trump administration in line with the tax blueprint released last year by Mr. Ryan and would reflect a more realistic approach to overhauling the tax code.

While Mr. Trump has promised the largest tax cut in history, political and fiscal realities have already begun to intervene.

The collapse of the Republican efforts to repeal the Affordable Care Act means that more than $1 trillion in taxes from that law, for the time being, are expected to remain in place. Republicans have also met fierce resistance to imposing a border adjustment tax on imports, and the opposition is growing louder to the elimination of the state and local income tax deduction for individuals.

Cutting the corporate tax rate to 15 percent from 35 percent would reduce tax revenue about $2 trillion over a decade, according to the Tax Foundation. It estimates that a reduction to 20 percent would reduce revenue by $1.6 trillion.

The constraints facing Republicans on tax reform were made plain on Tuesday when the House Budget Committee released a budget resolution outline that, if passed, would unlock the legislative tool that would let Republicans rewrite the tax code without the help of Democrats. The resolution requires that changes to the tax code do not add to the deficit.

Lawmakers in the House and Senate have been holding hearings this week as they prepare for tax reform. It was evident that Republicans continue to disagree on the best way to broaden the tax base so that they could set a corporate tax rate that is low enough to make the United States more competitive with other countries around the world. Most of the major economic powers have a corporate rate that is half the rate in the United States.

In a sign that Republican leaders may have learned some lessons from the health care debacle, Mr. Ryan is taking his tax pitch on the road this week. On Thursday, he will visit a sneaker factory in Massachusetts where he will make the case that rewriting the tax code is the key to improving the fortunes of American manufacturers.